ISA 444/544: Business Forecasting

class: center, middle, inverse, title-slide

.title[
# ISA 444/544: Business Forecasting
]
.subtitle[
## 07: Visualizing Many Time-Series
]
.author[
### <br>Fadel M. Megahed, PhD <br><br> Raymond E. Glos Professor in Business <br> Farmer School of Business<br> Miami University<br><br> <a href="https://twitter.com/FadelMegahed"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z" /></svg> <span class="citation">@FadelMegahed</span></a> <br> <a href="https://github.com/fmegahed/"><svg viewBox="0 0 496 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" /></svg> fmegahed</a> <br> <a href="mailto:fmegahed@miamioh.edu"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z" /></svg> fmegahed@miamioh.edu</a><br> <a href="https://calendly.com/fmegahed"><svg viewBox="0 0 384 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M202.021 0C122.202 0 70.503 32.703 29.914 91.026c-7.363 10.58-5.093 25.086 5.178 32.874l43.138 32.709c10.373 7.865 25.132 6.026 33.253-4.148 25.049-31.381 43.63-49.449 82.757-49.449 30.764 0 68.816 19.799 68.816 49.631 0 22.552-18.617 34.134-48.993 51.164-35.423 19.86-82.299 44.576-82.299 106.405V320c0 13.255 10.745 24 24 24h72.471c13.255 0 24-10.745 24-24v-5.773c0-42.86 125.268-44.645 125.268-160.627C377.504 66.256 286.902 0 202.021 0zM192 373.459c-38.196 0-69.271 31.075-69.271 69.271 0 38.195 31.075 69.27 69.271 69.27s69.271-31.075 69.271-69.271-31.075-69.27-69.271-69.27z" /></svg> Automated Scheduler for Office Hours</a><br><br>
]
.date[
### Fall 2025
]

---

## Quick Refresher of Last Class

✅ Describe and compute centered moving averages

✅ Estimate trend-cycle via moving averages

✅ Perform classical decomposition (trend-cycle, seasonal, residual/remainder)

✅ Understand STL / MSTL as alternatives to classical decomposition

---

## Learning Objectives for Today's Class

- Explain the differences between wide vs. long format

- Use [seaborn](https://seaborn.pydata.org/generated/seaborn.relplot.html) to plot multiple time-series

- Convert a data set to Nixtla's long format (`unique_id`, `ds`, `y`)

- Use [UtilsForecast](https://nixtlaverse.nixtla.io/utilsforecast/index.html) to visualize multiple series

---
class: inverse, center, middle

# Wide Vs. Long Format

---

## Wide Format

|Date       | Temperature (°F)| Muggy Days| Rainy/Snowy Days|
|:----------|----------------:|----------:|----------------:|
|2024-01-01 |               31|        0.0|                7|
|2024-02-01 |               34|        0.0|                6|
|2024-03-01 |               44|        0.0|                9|
|2024-04-01 |               54|        0.1|               10|
|2024-05-01 |               64|        3.4|               12|
|2024-06-01 |               72|       12.3|               11|
|2024-07-01 |               76|       18.2|               11|
|2024-08-01 |               74|       15.5|                9|
|2024-09-01 |               67|        7.0|                7|
|2024-10-01 |               55|        0.9|                7|
|2024-11-01 |               45|        0.0|                7|
|2024-12-01 |               35|        0.0|                8|

---

## Characteristics of Wide TS Data

- Each row represents a single observation

- Each column represents a different time series

- Easy to read and understand  (but not appropriate for analysis if you are using the [nixtlaverse](http://nixtlaverse.nixtla.io/statsforecast/docs/getting-started/getting_started_complete.html) group of Python packages)

---

## Long Format

|Date       |Variable         | Value|
|:----------|:----------------|-----:|
|2024-01-01 |Muggy Days       |   0.0|
|2024-01-01 |Rainy/Snowy Days |   7.0|
|2024-01-01 |Temperature (°F) |  31.0|
|2024-02-01 |Muggy Days       |   0.0|
|2024-02-01 |Rainy/Snowy Days |   6.0|
|2024-02-01 |Temperature (°F) |  34.0|
|2024-03-01 |Muggy Days       |   0.0|
|2024-03-01 |Rainy/Snowy Days |   9.0|
|2024-03-01 |Temperature (°F) |  44.0|
|2024-04-01 |Muggy Days       |   0.1|
|2024-04-01 |Rainy/Snowy Days |  10.0|
|2024-04-01 |Temperature (°F) |  54.0|

---

## Characteristics of Long TS Data

- Observations are now split into multiple rows

- Variable ids/labels are stored in a single column, and their corresponding values are stored in another column

- Easy to analyze and visualize (especially with the [nixtlaverse](http://nixtlaverse.nixtla.io/statsforecast/docs/getting-started/getting_started_complete.html) group of Python packages)

---

## A Visual Comparison

---

## Class Activity: From Wide to Long Format

.panelset[

.panel[.panel-name[Description]

In this activity, you will extract the adjusted closing prices of five stocks (AAPL, MSFT, GOOGL, AMZN, TSLA) from Yahoo Finance. Once you extract the data, you should **report** the following:  
  - **Summary statistics** of the **adjusted closing prices for each stock**.  
  - **Convert the data** from wide **to long format**, and **report the shape** of the long format data.  
  - **Save** the long format data to a CSV file.

**Hint:** Read and convert the column names prior to converting the data to long format.  
]

.panel[.panel-name[Starter Code]

``` python
import datetime as dt
import yfinance as yf
import pandas as pd

.panel[.panel-name[Notes]

.can-edit.key-activity8_logic[

**Please feel free to take any notes here from our in-class discussion and solution:** .font70[(Insert below)]

- Edit me  
  
  - ... 
  
  - ...  
  
  - ...
]
]
]

---
class: inverse, center, middle

# Visualizing Multiple Time-Series Using Seaborn

---

## Recall: Seaborn's `relplot` Function

---

## Seaborn's `relplot` Function with Wide Data

.pull-left-2[

.font90[

``` python
import datetime as dt
import yfinance as yf
import pandas as pd
import seaborn as sns

# Download the stock data for the following companies
stock_data = (
  yf.download(
    ['AAPL', 'MSFT', 'GOOGL', 'AMZN', 'TSLA'], 
    start='2020-01-01', 
    end= (dt.datetime.now().date() - dt.timedelta(days=1))
  )
  # Keep only the adjusted closing price
  [['Close']].reset_index()
)
  
# Overwrite the multi-index column names w/ single level
stock_data.columns = (
  ['Date', 'AAPL', 'MSFT', 'GOOGL', 'AMZN', 'TSLA'] )

# Plot the closing prices
sns.relplot(
  data=stock_data, kind='line', palette ='Paired'
)
```
]
]

.pull-right-2[

<img src="data:image/png;base64,#07_many_ts_files/figure-html/seaborn_wide_data_out-1.png" width="100%" style="display: block; margin: auto;" />
]

---

## Seaborn's `relplot` Function with Long Data

.font90[

``` python
import datetime as dt
import yfinance as yf
import pandas as pd
import seaborn as sns

stock_data = (
  yf.download(
    ['AAPL', 'MSFT', 'GOOGL', 'AMZN', 'TSLA'],  
    start='2020-01-01', end= (dt.datetime.now().date() - dt.timedelta(days=1))
  )
  # Keep only the adjusted closing price
  [['Close']].reset_index()
  # Rename the column axis within the method chaining (adv)
  .pipe( lambda df: df.set_axis(['Date', 'AAPL', 'MSFT', 'GOOGL', 'AMZN', 'TSLA'], axis=1) )
  # Convert to long format
  .melt(id_vars='Date', var_name='Stock', value_name='Close')
)

# Plot the adjusted closing prices
fig = sns.relplot(
  data=stock_data, x='Date', y='Close', kind='line', legend=False, hue='Stock', 
  palette='Paired',
)
plt.tight_layout() # improves title visibility
```
]

---
count: false

## Seaborn's `relplot` Function with Long Data

---

## Seaborn's `relplot` Function with Long Data (Facets)

.font90[

``` python
import datetime as dt
import yfinance as yf
import pandas as pd
import seaborn as sns

# Plot the adjusted closing prices
fig = sns.relplot(
  data=stock_data, x='Date', y='Close', kind='line', legend=False, hue='Stock', col='Stock',
  palette='Paired', col_wrap=2,  facet_kws={'sharey': False, 'sharex': False}
)
plt.tight_layout() # improves title visibility
```
]

---
count: false

## Seaborn's `relplot` Function with Long Data (Facets)

---

## Activity: Reflect on the Previous Seaborn Plots

- Whether you are plotting multiple lines in a single plot or using facets, the `relplot` function is quite versatile. However, this approach is only suitable for a few (in my opinion `\(\le 9\)` time series). **So what options, do we have if we have more than 9 time series?**

- I think there are **three alternative charting approaches** (I am not talking about specific libraries). **Can you guess what they are?**

.can-edit.key-activity9_logic[  
  + In the next three minutes, edit the bullet points below to reflect the three alternative charting approaches.

+ ...

+ ...  
  
  + ...
]

---
class: inverse, center, middle

# Advanced Visualizations with Seaborn

---

## Approach 1: Sample

- **Sample** a subset of the time series to plot. This approach is useful when you have a large number of time series and you want to visualize a **representative sample**.

- **Key Point:**  The sample should be **representative** of the entire data set.

---

## Approach 1: Sample (Code Example)

.font90[

``` python
import pandas as pd
import seaborn as sns
import random

*random.seed(2025) # for reproducibility

# Start with the long format data and sample two stocks
*sampled_stocks = stock_data['Stock'].unique().tolist()
*sampled_stocks = random.sample(sampled_stocks, 2)

# Plot the adjusted closing prices
fig = sns.relplot(
* data=stock_data.query('Stock in @sampled_stocks'),
  x='Date', y='Close', kind='line', legend=False, hue='Stock', col='Stock',
  palette='Paired', col_wrap=2,  facet_kws={'sharey': False, 'sharex': False}
)
plt.tight_layout() # improves title visibility
```
]

---

## Appraoch 1: Sample (Result)

---

## Approach 2: Animated Plots

- **Animate** the time series data. This approach is useful when you have a large number of time series and you want to visualize all of them.

- **Key Point:**  Animated plots can be **interactive** and **engaging**.

---

## Approach 2: Animated Plots (Code Example)

.font90[

``` python
import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns
import imageio.v2 as imageio

# Start with long format data
stocks = stock_data['Stock'].unique().tolist()

image_paths = []

for stock in stocks:
    sns.relplot(
      data=stock_data.query('Stock == @stock'), kind ='line',
      x='Date', y='Close', color ='black',
      height = 4, aspect = 3
    )
    plt.title(f"Adjusted Closing Price of {stock} (2020-2025)", fontsize=14)
    plt.xlabel("Date", fontsize=12)
    plt.ylabel("Adjusted Closing Price", fontsize=12)
    plt.tight_layout()
    plt.savefig(f'../../figures/{stock}_animated_plot.png')
    image_paths.append(f'../../figures/{stock}_animated_plot.png')
    
# Create a GIF from the images
images = [imageio.imread(path) for path in image_paths]
imageio.mimsave('../../figures/animated_stock_lineplot.gif', images, fps=0.25)
```

<img src="data:image/png;base64,#07_many_ts_files/figure-html/seaborn_animated-9.png" width="1152" style="display: block; margin: auto;" />
]

---

## Approach 2: Animated Plots (Result)

---

## Approach 3: Spaghetti Plot

- **Plot all time series** on a single plot. This approach is useful when you have a large number of time series and you want to visualize all of them.

- **Key Points:**   
  + Use **light gray** for the lines to **de-emphasize** individual time series.  
  + Use **bold colors** for the lines of **specific time series (or summary statistics across all time series)** to **emphasize** them.

---

## Approach 3: Spaghetti Plot (Code Example)

.font90[

``` python
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

# for each stock, plot the closing price over time as a light gray line
for stock, group in stock_data.groupby("Stock"):
  ax = sns.lineplot(data=group, x='Date', y='Close', color='lightgray', alpha=0.5)

# Calculate and overlay percentiles across all time series for each date
quantiles = stock_data.groupby('Date')['Close'].quantile([0.05, 0.5, 0.95]).unstack()

# Plot the median, 5th, and 95th percentiles
sns.lineplot(data=quantiles, x=quantiles.index, y=0.5, color='black', label='Median', ax = ax)
sns.lineplot(data=quantiles, x=quantiles.index, y=0.05, color='blue', label='5%', ax=ax)
sns.lineplot(data=quantiles, x=quantiles.index, y=0.95, color='red', label='95%', ax=ax)
```
]

---

## Approach 3: Spaghetti Plot (Result)

---
class: inverse, center, middle

# Nixtla's Long Format

---

## Class Activity: Convert Data to Nixtla's Format

- **Data:** [This COVID-19 data set](https://miamioh.instructure.com/courses/240425/files/36714508?module_item_id=6207531) contains the daily cumulative number of confirmed cases for each county.

- **Objectives:**   
  + Read the data set.  
  + Filter the data to include only the 88 counties in Ohio, and dates from 2020-04-01 to 2022-12-31.  
  + Convert the data to Nixtla's long format (`unique_id`, `ds`, `y`), where the:  
      + `unique_id` column is used to identify each county.  
      + `ds` column is used to represent the date.  
      + `y` column is used to represent the cumulative number of confirmed cases.
  + Use the `plot_series` method from the [UtilsForecast](https://nixtlaverse.nixtla.io/utilsforecast/index.html) to visualize the data. See [here](https://nixtlaverse.nixtla.io/utilsforecast/index.html) to learn about how to import and [here](https://nixtlaverse.nixtla.io/utilsforecast/plotting.html) to see the arguments of the `plot_series` method.

---

class: inverse, center, middle

# Recap

---

## Summary of Main Points

By now, you should be able to do the following:

- Explain the differences between wide vs. long format

- Use [seaborn](https://seaborn.pydata.org/generated/seaborn.relplot.html) to plot multiple time-series

- Convert a data set to Nixtla's long format (`unique_id`, `ds`, `y`)

- Use [UtilsForecast](https://nixtlaverse.nixtla.io/utilsforecast/index.html) to visualize multiple series

---

## 📝 Review and Clarification 📝

1. **Class Notes**: Take some time to revisit your class notes for key insights and concepts.
2. **Zoom Recording**: The recording of today's class will be made available on Canvas approximately 3-4 hours after the session ends.
3. **Questions**: Please don't hesitate to ask for clarification on any topics discussed in class. It's crucial not to let questions accumulate.